Question

Having a conceptual problem

why is 0/0 undefined?

Answer 1

@Callisto @TuringTest please help ...

Answer 2

0/0 is not undefined...it is indeterminate

Answer 3

indeterminate

Answer 4

what that does mean actually? @lgbasallote

Answer 5

this is not an easy question to answer
it has to do with different ways you can approach this limit

Answer 6

the value cannot be determined...thus INdeterminate

Answer 7

Oh no problem @TuringTest , I understand the problem

@lgbasallote thanks a lot

Answer 8

there are a few main reasons why:

1) it conflicts between the rule that a number divided by itself is 1; and the rule that 0 divided by anything is 0. thus it conflicts whether the value is 1 or 0. so you cant determine if it is 1 or 0.

2) another reason is because there are infinite values that will give you 0 when multiplied by 0. so you cant determine which number is the right one.

Answer 9

Well @mathslover Recommend this site ..

how to use this?

Answer 10

already sent him info on indeterminate

Answer 11

for example\[\lim_{x\to0}\frac xx=1\]but\[\lim_{x\to0}\frac{2x}x=2\]but both are mathematically equivalent to \[\frac00\]in the l;imit
hence if we admitted\[\frac00\]into the set of numbers and gave it a value it would be inconsistent in mathematics and destroy the whole system effectively.

Answer 12

\[\lim_{x\to0}\frac{x^2}x=0\]etc.
it would be an "inconsistent formal system"

Answer 13

to easily understand this concept let's take an example of (10/2) which is same as 5, and (5/5) is same as 1, but we can't say (0/0) as 1 simply because 0 on numerator is equal to zero on denominator, and (0/0) is undefined..... we don't know what it is.

Answer 14

@SUROJ (0/0) is not undefined

Answer 15

undefined is x/0

Answer 16

@lgbasallote why x/0 is undefined? curious

Answer 17

okay let's say for example x = 2

2/0

can you give me a number that when you multiply to 0 the answer is 2?

Answer 18

I think that technically both are undefined
1/0 is undefined but *not* an indefinite form
0/0 is an indefinite form. Is it also undefined? I think so...

Answer 19

nope

Answer 20

i think the best term for 0/0 is indeterminate..

Answer 21

any division by zero is undefined, so

x/0 is undefined
1/0 undefined and not indefinite
0/0 undefined and indefinite

that's my understanding

Answer 22

my way of thinking is undefined refers to an infinite number that is not defined but we relatively know its really big or really small(big negative)
indeterminate means we have no idea what the value is

Answer 23

I meant "indeterminate" when I said "indefinite" :/
so do you say that 1/0 is indeterminate or not?

Answer 24

@dumbcow

Answer 25

no i would say its not indeterminate because we know the limit of 1/x as x->0 is infinity

Answer 26

1/0 is not indeterminate

Answer 27

ok I agree with that
just making sure we're all on the same page

Answer 28

0*1 = 0
0*2 = 0
0*dog = 0
0*nitinz570 = 0

can you tell particularly for what values you are getting 0..??

Answer 29

the indeterminate forms are:
0/0
inf/inf
0*inf

Answer 30

1/0 is complex infinity

Answer 31

0^0 debated at times

Answer 32

\(0^0\) is also undetermined..

Answer 33

yep

Answer 34

indeterminate*

Answer 35

see how the mayan's gave mathematicians more to debate about?

Answer 36

there are 7 indeterminate forms in nature

Answer 37

just check wolfram mathworld.

Answer 38

mathematicians debate whether or not \(0^0=1\) or not
Euler, for instance, thought it did

Answer 39

0/0, infinity/infinity, 0^infinity, 1^infinity, 0^0, infinity^0, infinity-infinity

Answer 40

if 0^0 =1 then 0/0 = 1 also

Answer 41

http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/?PHPSESSID=40fdcce21f158a5d17267b711e395947#b
not true panlac

Answer 42

http://mathworld.wolfram.com/Indeterminate.html

Answer 43

mathematicians *define* \(0^0=1\) because of a number of arguments
btw note that your reference is
Thomas and Finney 1996, pp. 220 and 423; Gellert et al. 1989, p. 400
and there are other equally reputable books and references that disagree if you read the article I linked you too, or some of those linked to it.

Answer 44

*some* mathematicians - I meant above...

Answer 45

it is just very debated ti this day is all
I generally treat it as undefined as well

Answer 46

to*

Answer 47

yeh. my math professor is one of those who thinks the same way. but she teaches it as indeterminate

Answer 48

It makes more sense to me as well, I'm just pointing out the discrepancy out there...

Answer 49

trust me, it does to me also

Answer 50

For x not equal to 0, x/0 is defined (as a number, not necessarily as a limit) in a 1-point compactification of the reals (the projectively extended real numbers) or the complex numbers (the extended complex plane), and is equal to infinity. However, 0/0 (as a number) is still undefined in these settings.

Answer 51

btw the limit of x^x as x->0 is 1 , which i believe is a strong argument for equating 0^0 to 1

Answer 52

Nice discussion and also :

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